Problem: Simplify the following expression: $k = \dfrac{60r^2 + 10r}{20r^2 + 50r} + \dfrac{30r^2}{20r^2 + 50r}$ You can assume $p,q,r \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{60r^2 + 10r + 30r^2}{20r^2 + 50r}$ $k = \dfrac{90r^2 + 10r}{20r^2 + 50r}$ The numerator and denominator have a common factor of $10r$, so we can simplify $k = \dfrac{9r + 1}{2r + 5}$